In square ABCD, P and Q are the midpoints of sides AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find the area of △OPB.
In square ABCD, P and Q are the midpoints of sides AB and CD respectively.
PQ and BD are joined which intersect each other at O.
Side of square AB = 8 cm
∴ Area of the square ABCD=(Side)2=82=64 cm2
∵ Diagonal BD bisects the square into two triangles equal in area
Area △ABD=12×Area of square ABCD
=12×64=32cm2
∵ P is mid point of AB of △ABD,
and PQ || AD
∴ O is the mid point of BD
∴OP=12AD=12×8=4cm∴Area of△OPB=12PB×OP=12×4×4=8cm2